Geometric Systems for Building 3-D Structures

ABSTRACT

Geometric systems for building 3-D structures from a plurality of 2-D building elements, including a first building element defining a first shape defined by edges with a first dimension, and a second building element defining a second shape incongruent to the first shape defined by edges with a second dimension incongruent to the first dimension. Further, each building element defines an imaginary circle having a center aligned with the center of the building element, and defines a plurality of notches positioned at and tangential to the circumference of the imaginary circle, where the plurality of building elements are configured to fit together at their respective notches to torn a 3-D structure. Geometric systems may include a first building element defining a first shape with a first contour, and a second building element defining a second shape incongruent to the first shape with a second contour incongruent to the first contour.

BACKGROUND

The present disclosure relates generally to geometric systems. Inparticular, geometric systems with interfitting building elements forbuilding structures are described.

The construction of 3-D structures from 2-D building elements is aneffective means for studying various geometric shapes, including, butnot limited to, Platonic, Archimedean, and Johnson solids as well asprisms, antiprisms, and various non-convex structures with regularfaces. This area of study also lends itself well to the understanding ofmathematical concepts associated with these geometric shapes and may aidin the development of the user's creative appetite. Indeed, geometricbuilding systems are an excellent means for constructing an infinitenumber of geometric shapes while exposing users to an activity thatintersects the world of art with the world of mathematics to makewonderful and colorful creations.

Known geometric systems are not entirely satisfactory for the range ofapplications in which they are employed. For example, existing geometricsystems do not allow for the interfitting or interconnection ofindividual incongruent elements to construct a 3-D structure. Inaddition, conventional geometric systems, because of their failure toallow the interconnection of incongruent elements, are limited to a verysmall subset of 3-D structures that can actually be constructed.

Thus, there exists a need for geometric systems that improve upon andadvance the design of known geometric systems. Examples of new anduseful geometric systems for building 3-D structures relevant to theneeds existing in the field are discussed below.

Disclosure addressing one or more of the identified existing needs isprovided in the detailed description below. Examples of referencesrelevant to geometric systems for building 3-D structures include U.S.Pat. Nos. 7,469,898; 5,593,337; 5,489,230; and U.S. Patent ApplicationPublication: 20120164912. However, each one of these references suffersfrom one or more of the following disadvantages: the individual buildingelements used to construct the 3-D structures can only be interconnectedwith other building elements that are exactly the same shape and thematerial from which these building elements are manufactured is limitedto either only flexible materials or only rigid materials, but never acombination of both types of material. The complete disclosures of theabove patents and patent applications are herein incorporated byreference for all purposes.

SUMMARY

The present disclosure is directed to geometric systems for building 3-Dstructures from a plurality of 2-D building elements, including a firstbuilding element defining a first shape defined by edges with a firstdimension, and a second building element defining a second shapeincongruent to the first shape defined by edges with a second dimensionincongruent to the first dimension. Further, each building elementdefines an imaginary circle haying a center aligned with the center ofthe building element and defines a plurality of notches positioned atthe circumference of the imaginary circle and aligned tangentially tothe imaginary circle and where the plurality of building elements,including the first banding element and the second building elementincongruent shapes, are configured to fit together at their respectivenotches to form a 3-D structure. In some examples, geometric systemsinclude a first building element defining a first shape defined by edgeswith a first contour, and a second building element defining a secondshape incongruent to the first shape defined by edges with a secondcontour incongruent to the first contour.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of a first example of a geometric systemdepicting two incongruent building elements interconnecting.

FIG. 2 is a perspective view of the geometric system shown in FIG. 1depicting two incongruent building elements interconnecting.

FIG. 3 is a perspective view of the geometric system illustrating fourincongruent building elements interconnecting.

FIG. 4 is a top plan view of two building elements, a first buildingelement at the top of the figure in the shape of triangle and havingnon-rectilinear notches and a second building element at the bottom ofthe figure in the shape of a triangle and having rectilinear notches.

FIG. 5 depicts the first building element and the second buildingelement shown in FIG. 4 with the first building element interconnectingwith the second building element by joining together the non rectilinearnotch of the first building element and the rectilinear notch of thesecond building element.

FIG. 6 is a top plan view of an example building element.

FIG. 7 is a top plan view of another example building element

FIG. 8 is a top plan view of another example building element.

FIG. 9 is a top plan view of another example building element.

FIG. 10 is a top plan view of another example building element.

FIG. 11 is a top plan view of another example building element.

FIG. 12 is a top plan view of a geometric system constructed from aplurality of building elements to form an octahedron structure.

FIG. 13 is a top plan view of a geometric system constructed from aplurality of building elements to form a cuboctahedron structure.

FIG. 14 is a top plan view of a geometric system constructed from aplurality of building elements to form a truncated icosahedronstructure.

DETAILED DESCRIPTION

The disclosed geometric systems will become better understood throughreview of the following detailed description in conjunction with thefigures. The detailed description and figures provide merely examples ofthe various inventions described herein. Those skilled in the art willunderstand that the disclosed examples may be varied, modified, andaltered without departing from the scope of the inventions describedherein. Many variations are contemplated for different applications anddesign considerations; however, for the sake of brevity, each and everycontemplated variation is not individually described in the followingdetailed description.

Throughout the following detailed description, examples of variousgeometric systems are provided. Related features in the examples may beidentical, similar, or dissimilar in different examples. For the sake ofbrevity, related features will not be redundantly explained in eachexample. Instead, the use of related feature names will cue the readerthat the feature with a related feature name may be similar to therelated feature in an example explained previously. Features specific toa given example will be described in that particular example. The readershould understand that a given feature need not be the same or similarto the specific portrayal of a related feature in any given figure orexample.

With reference to FIGS. 1-14, a geometric system 18 for building 3-Dstructures will now be described. Geometric system 18 includes a firstbuilding element 20 and a second building element 30. The reader shouldunderstand that geometric systems described herein may include aplurality of building elements, such as 2, 3, 5, 10, 50, or 100 or morebuilding elements.

In use, as shown in FIGS. 1-3, 5, and 12-14, two or more buildingelements are interconnected together to form a three-dimensional (3-D)structure. In some examples, the geometric system forms a 3-D structurein the form of a polyhedron whereas in other examples, the system formsan irregular 3-D structure. The user's imagination and skill will leadto a variety of 3-D shapes, which adds to the enjoyment and learningpossible with the geometric systems described herein.

For example, the geometric systems described herein may form Platonicsolids, Archimedean solids, and Johnson solids by interconnectingbuilding elements together. Alternatively, a user may interconnectbuilding elements to each other to form a variety of 3-D polyhedrons orother 3-D structures. Of course, substantially planar structures may becreated with geometric systems described herein as well, which might beconsidered two-dimensional given the relative dimensions of theresulting structure.

In many examples, the building elements are made from a lightweight,inexpensive material, such as paper, which leads to 3-D structures thatare aesthetically pleasing, but not structurally sound. However, in someexamples, the building elements are made from structurally significantmaterials, such as wood, hard plastic, metal, or other rigid material,and may be used to construct 3-D structures with structural integrity.For instance, geometric systems including structural building elementsmay form enhanced 3-D structures such as lamps, toys, or even morepermanent structures as part of an arts and crafts kit.

The plurality of building elements may be the same share and/orconfiguration, as shown in FIG. 2, or may include one or more differentshapes and/or configurations, as shown on FIGS. 1, and 3-5, In someexamples, the building elements are each a different shape and/orconfiguration from the other building elements within the plurality ofbuilding elements. In other examples, the plurality of building elementsincludes a mix of building elements that are congruent to other buildingelements and incongruent to other building elements in the plurality orset of building elements making up the geometric system.

FIGS. 4 and 5 demonstrate one example what is meant by a differentconfiguration: the reader can see that the building element in FIGS. 4and 5 are the same shape when viewed in profile, but are configureddifferently with regard to the shape of heir notches. In FIG. 4, abuilding element 120 is shown at the top of the figure in the shape of atriangle with edges 124 and non-rectilinear notches 126. Buildingelement 130 is shown at the bottom of FIG. 4 and is in the shape of atriangle with edges 134 and rectilinear notches 136.

Turning attention to FIG. 1, building element 20 defines a firstgeometric shape 22, a 3-pointed star, defined by outer edges 24. Whilebuilding element 20 is technically three-dimensional in that it has alength, a width, and a thickness, it may be referred to as substantiallytwo-dimensional (2-D) given that its thickness is significantly smallerthan its length and width. In other examples, the building element mayhave a thickness that is larger and in those instances the buildingelement may be considered a three-dimensional component.

Building element 20 defines an imaginary circle haying a center alignedwith the center of building element 20. In the example shown in FIG. 1,building element defines an aperture 28 in the shape of a circle that isalso aligned with the center of the building element. However, in someexamples the building element does not define an aperture in the shapeof a circle, but instead defines an aperture of another shape, such as atriangle, square, another regular polygon, or an irregular polygon.Aperture 26 may assist users to hold and manipulate building element 20while constructing 3-D structures, In some examples, the buildingelement does not define an aperture.

Building element 20 defines three notches 26. In certain examples, thebuilding element includes less than three notches, such as one or twonotches. In still further examples, the building element includes morethan three notches, such as four, five, or six or more notches.

Notches 26 are substantially rectilinear in shape as compared to notches126 shown in FIG. 4, which are non rectilinear in shape. In variousexamples, the building element may define rectilinear notches,non-rectilinear notches, or a combination of rectilinear andnon-rectilinear notches. In the example shown in FIGS. 1 and 2, notches26 are proximally disposed to the circumference of the imaginary circleand aligned tangentially to the imaginary circle.

In the example shown in FIGS. 1 and 2, building element 20 has a firstsize. In some examples, the geometric system may include buildingelements with the same shape, but a different size than building element20. The building elements having the same shape as building element 20may be larger and smaller than building element 20.

Building element 20 may be manufactured from such materials as foam,ethylene vinyl acetate, poster board, or laminated paper. Additionallyor alternatively, the building elements of the present invention may bemanufactured from wood veneer, acrylic, or sisal. The reader shouldunderstand that the building elements described herein may bemanufactured from virtually any material currently known or yet to bediscovered that would allow the building elements to interconnect andform 3-D structures.

Continuing with FIG. 1, another building element, building element 30,will be described. Building element 30 in FIG. 1 and the other buildingelements described herein, such as those shown in FIGS. 3-14, aresimilar in some respects to building element 20 and different in otherrespects. Accordingly, the distinctions between the building elementswill be highlighted and the reader should understand that the featuresand contemplated variations of building element 20 described above mayapply to the other building elements described herein.

As shown in FIG. 1, building element 30 defines a second geometric shape32, a 6-pointed star, with outer edges 34. Building element 30 is largerthan building element 20. Building element 30 defines an imaginarycircle having a center aligned with the center of building element 30.Building element 30 further defiles a centrally positioned aperture 33in the shape of a circle. As shown in FIG. 1, building element 30defines three notches 36 that are rectilinear in shape and areproximally disposed to the circumference of the imaginary circle andaligned tangentially to the imaginary circle.

The reader can see in FIG. 1 that building element 30 is incongruent tobuilding element 20. However, building elements 20 and 30 can beinterconnected through their respective notches 36 and 26 to form a 3-Dstructure. Alternatively, in other examples, such as shown in FIG. 2,building elements that are congruent may also be interconnected viatheir notches. As further shown in FIGS. 3, 5, and 12-14, geometricsystems described herein may include a variety of interconnectedbuilding elements, some congruent and some incongruent, to form 3-Dstructures.

Interconnecting incongruent building elements, such as building element20 and building element 30, may facilitated by forming notches 26 and 36to be of equal length. Further, placing notches 26 and 36 proximate thecircumference of the imaginary circles centered on the building elementshelps enable a user to construct 3-D structures having regular faces,i.e., faces that are equiangular and equilateral. Having a plurality ofbuilding elements, each with notches oriented proximate thecircumference of an imaginary circle centered on the building element,enable a user to interconnect an large number of building elements,whether the building elements are congruent or incongruent to oneanother, such as shown in see FIG. 3. Different building elementsdefining different shapes and different numbers of notches with respectto other building elements in the geometric system allows a user toconstruct a wide variety of 3-D structures.

Turning attention to FIG. 4, a second example of a geometric system 118will now be described. Geometric system 118 includes mares similar oridentical features to geometric system 18. Thus, for the sake ofbrevity, each feature of geometric system 118 will not be redundantlyexplained. Rather, key distinctions between geometric system 118 andgeometric system 18 will be described in detail and the reader shouldreference the discussion above for features substantially similarbetween the two geometric systems.

As can be seen in FIG. 4, geometric system 118 includes a buildingelement 120 and a building element 130. Building elements 120 and 130define a plurality of notches 126 and 136 and a plurality of edges 124and 134, respectively. Here, geometric system 118 differs from geometricsystem 18 in building elements 120 and 130 define a substantiallysimilar shape when viewed in profile, namely, a triangle, but thebuilding elements are configured differently. In particular, buildingelement 120 defines a plurality of non-rectilinear notches 126 whereasbuilding element 130 defines rectilinear notches 136.

FIG. 4 illustrates that notches 126 are non-rectilinear, but stillconfigured to be interconnected with rectilinear notches 136 of buildingelement 130. This is possible because of the location of non-rectilinearnotches 136 relative to building element 130. Non-rectilinear notches126 of building element 120 are disposed proximate the circumference ofthe imaginary circle centered on the building element and alignedtangentially to the imaginary circle as in building element 20. Theplacement of the notches, whether rectilinear or non-rectilinear,proximate the circumference of the imaginary circle relative to eachgeometric shape allows different building elements with the same ordifferent shape profile to interconnect with each other, such as shownin FIG. 5.

Turning attention to FIG. 6, additional building elements that may beadded to both. geometric system 18 and geometric system 118 will now bedescribed. The additional building elements include similar or identicalto the building elements included in geometric system 18 and geometricsystem 118. Thus, for the sake of brevity, each feature the additionalbuilding elements will not be redundantly explained. Rather, keydistinctions between these additional building elements and the buildingelements from geometric system 18 and geometric system 118 will bedescribed in detail and the reader should reference the discussion abovefor features substantially similar between the additional buildingelements and the building elements of system 18 and system 118.

As can be seen in FIG. 6, a building element 320 defines a thirdgeometric shape 322, a 4-pointed star, with edges 324. Building element320 defines a plurality of notches 326 and an aperture 328. The primarydifference between building element 20 and building element 320 is theirrespective shapes. Building element 20 defines a first geometric shape22, which is a 3-pointed star, and building element 320 defines a thirdgeometric shape 322, which is a 4-pointed star.

Turning attention to FIG. 7, a building element 420 defuses a fourthgeometric shape 422, a 6-pointed star, with edges 424. Building element420 defines a plurality of notches 426 and an aperture 428, The maindifference between building element 20 and building element 420 is theirrespective shapes. Building element 20 defines a first geometric shape22, which is a 3-pointed star and building element 420 defines a fourthgeometric shape 422, which is a 6-pointed star.

Turning attention to FIG. 8, a building element 720 defines a fifthgeometric shape 722, a triangle, with edges 724. Building element 720includes a plurality of edge tabs 725 and a plurality of notches 726.Differences between building element 20 and building element 720 includetheir respective shapes and the addition of edge tabs 725 in buildingelement 720. Building element 20 defines a 3-pointed star and buildingelement 720 defines a fifth geometric shape, which is a triangle.

As shown in FIG. 8, tab 725 is a semicircular-shaped tab that isintegrally formed with edge 724. Tab 725 is positioned with asemicircular portion 727 extending away from edge 724. A flat edge 728of tab 725 cooperates with edge 724 to form a rectilinear notch 726.Alternatively, in other examples, the flat edge of the semicircular taband edge may cooperate to form a non rectilinear notch.

Shifting to FIG. 9, a building element 820 defines a sixth geometricshape 822, a square, and includes edges 824. Building element 820includes a plurality of tabs 825 and a plurality of notches 826, Theprimary difference between building element 720 and building element 820is their respective shapes. Building element 720 defines a triangle andbuilding element 820 defines a square.

Building element 820 also includes a plurality of semicircular tabs 825that are integrally formed with edges 824 and positioned with asemicircular portion 827 of tab 825 extending away from edge 824. A flatedge 828 of tab 825 cooperates with edge 824 to form a rectilinear notch826. Alternatively, the flat edge of the semicircular tab and edge maycooperate to form a non-rectilinear notch.

FIGS. 10 and 11 detail two more variations of the nearly unlimitedshapes that can be used with the present invention to construct 3-Dpolyhedrons. FIG. 10 illustrates a building element 520 that defines aseventh shape 522 that resembles a variation of a 4-pointed star. FIG.11 illustrates a building element 620 that defines an eighth shape 622that resembles a 5-pointed leaf,

FIGS. 12 through 14 illustrate three of the virtually unlimited possiblestructures that can be constructed with the geometric systems describedherein. FIG. 12 illustrates an octahedron 900 constructed from eightbuilding elements 22, which define 3-pointed stars. FIG. 13 illustratesa cuboctahedron 1000 constructed from eight building elements 22, whichdefine 3-pointed stars, and six building elements 322, which define4-pointed stars. FIG. 14 illustrates a truncated icosahedron 1100constructed from 12 building elements 30, which define 5-sided stars and20 building elements 420, which define 6-sided stars.

The disclosure above encompasses multiple distinct inventions withindependent utility. While each of these inventions has been disclosedin a particular form, the specific embodiments disclosed and illustratedabove are not to be considered in a limiting sense as numerousvariations are possible. The subject matter of the inventions includesall novel and non-obvious combinations and subcombinations of thevarious elements, features, functions and/or properties disclosed aboveand inherent to those skilled in the art pertaining to such inventions.Where the disclosure or subsequently filed claims recite “a” element, “afirst” element, or any such equivalent term, the disclosure or claimsshould be understood to incorporate one or more such elements, neitherrequiring nor excluding two or more such elements.

Applicant(s) reserves the right to submit claims directed tocombinations and subcombinations of the disclosed inventions that arebelieved to be novel and non-obvious. Inventions embodied inn othercombinations and subcombinations of features, functions, elements and/orproperties may be claimed through amendment of those claims orpresentation of new claims in the present application or in a relatedapplication. Such amended or new claims, whether they are directed tothe same invention or a different invention and whether they aredifferent, broader, narrower or equal in scope to the original claims,are to be considered within the subject matter of the inventionsdescribed herein.

We Claim:
 1. A geometric system for building 3-D structures.,comprising: a plurality of 2-D building elements configured to connecttogether for building 3-D structures, including: a first buildingelement defining a first shape defined edges with a first dimension, anda second building element defining a second shape incongruent to thefirst shape defined by edges with a second dimension incongruent to thefirst dimension; and where each building element: defines an imaginarycircle having a center aligned with the center of the building element,and defines a plurality of notches disposed at the circumference of theimaginary circle and aligned tangentially to the imaginary circle; andwhere the plurality of building elements, including the first buildingelement and the second building element defining incongruent shapes, areconfigured to fit together at their respective notches to form a 3-Dstructure.
 2. The geometric system of claim 1, wherein the plurality ofnotches are rectilinear for the first building element andnon-rectilinear for the second building element.
 3. The geometric systemof claim 1, wherein the plurality of notches are arbitrarily rectilinearand non-rectilinear in shape for all of the interconnected 2-D buildingelements.
 4. The geometric system of claim 1, wherein the notches ofeach building element to be interconnected are of equal length.
 5. Thegeometric system of claim 1, wherein the distance from the notches tothe center of the building elements is selected to cause the pluralityof building elements to form a 3-D structure having faces that areequiangular and equilateral hen interconnected.
 6. The geometric systemof claim 1, wherein the location of the notches in relation to thecenter of each building element is selected to cause the plurality ofbuilding elements to form a 3-D Platonic structure, a 3-D Johnsonstructure, or a 3-D Archimedean structure when interconnected.
 7. Thegeometric system of claim 1, wherein the 2-D building elements are madefrom ethylene vinyl acetate, poster board, or laminated paper.
 8. Thegeometric system of claim 1, wherein the 2-D building elements are madefrom wood veneer, acrylic, or sisal.
 9. The geometric system of claim 1,wherein the edges of the 2-D building elements are curvilinear.
 10. Ageometric system for building 3-D structures from a plurality of 2-Dbuilding elements, comprising: a plurality of 2-D building elementsconfigured to connect together for building 3-D structures, including: afirst building element defining a first shape defined by edges with afirst contour, and a second building element defining a second shapeincongruent to the first shape defined by edges with a second contourincongruent to the first contour; and where each building element:defines an imaginary circle having a center aligned with the center ofthe building element, and defines a Plurality of notches disposed at thecircumference of the imaginary circle and aligned tangentially to theimaginary circle; and where the plurality of building elements,including the first building element and the second building elementdefining incongruent shapes, are configured to fit together at theirrespective notches to form a polyhedron structure.
 11. The geometricsystem of claim 10, wherein the plurality of notches are rectilinear forthe first building element and non-rectilinear for the second buildingelement.
 12. The geometric system of claim 10, wherein each 2-D buildingelement is configured with at least three notches.
 13. The geometricsystem of claim 10, wherein the plurality of notches arenon-rectilinear, allowing the interconnection of 2-D building elementsthat are made of various materials.
 14. The geometric system of claim10, wherein the notches of each 2-D building element to beinterconnected are of equal length.
 15. The geometric system of claim10, wherein incongruent 2-D building elements are configured to havenotches of the same length and to interconnect to form a 3-D Platonicpolyhedron, a 3-D Johnson polyhedron, or a 3-D Archimedean polyhedron.16. The geometric system of claim 10, wherein the distance from thenotches to the center of the building elements is selected to cause theplurality of building elements to form a 3-D structure having faces thatare equiangular and equilateral when interconnected.
 17. The geometricsystem of claim 10, further comprising a plurality of edge tabs, theedge tabs being integrally formed with the edges of the 2-D buildingelements to form the notches.
 18. The geometric system of claim 10,wherein the contours of the 2-D building elements are curvilinear. 19.The geometric system of claim 10, wherein the 2-D building elements aremade from ethylene vinyl acetate, poster board, or laminated paper. 20.The geometric system of claim 10, wherein the 2-D building elements aremade from wood veneer, acrylic, or sisal.